What will come in place of the question mark (?) in the following numbers ?
12 14 17 13 8 14 21 13 4 ?

Options

A. 14
B. 13
C. 15
D. 2

Answer

To solve the problem of finding the number that will replace the question mark (?) in the sequence: 12, 14, 17, 13, 8, 14, 21, 13, 4, ?, we will analyze the pattern of the sequence step by step.

### Step-by-Step Solution:

1. **Identify the Sequence**: Write down the numbers in the sequence:
- 12, 14, 17, 13, 8, 14, 21, 13, 4, ?

2. **Calculate Differences**: Find the differences between consecutive numbers:
- 14 - 12 = +2
- 17 - 14 = +3
- 13 - 17 = -4
- 8 - 13 = -5
- 14 - 8 = +6
- 21 - 14 = +7
- 13 - 21 = -8
- 4 - 13 = -9

So, the differences are: +2, +3, -4, -5, +6, +7, -8, -9.

3. **Analyze the Pattern of Differences**:
- The differences alternate between increasing and decreasing.
- The increasing differences are +2, +3, +6, +7 (which are increasing by 1 each time).
- The decreasing differences are -4, -5, -8, -9 (which are decreasing by 1 each time).

4. **Predict the Next Difference**:
- Following the pattern, the next difference after -9 should be -10 (continuing the decreasing sequence).

5. **Calculate the Next Number**:
- Now, apply the predicted difference of -10 to the last number in the sequence (which is 4):
- 4 - 10 = -6.

6. **Conclusion**:
- Therefore, the number that will come in place of the question mark (?) is -6.

### Final Answer:
The answer is -6.